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| − | + | The stationary increment property says that the difference between the values of a random process at two distinct times will result in a random variable with the same distribution as the random variable contained in the random process at the time found by differencing the two distinct times mentioned earlier. | |
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| + | Sum processes have this property because the difference between the values of a sum process at two distinct times yields a random variable defined by summing the values of an iid process from the earlier time until the later time. In addition, the random variable contained in the sum process at the time found by differencing the earlier and later times is found by summing the values of the same iid process from the initial time until the time found by differencing the earlier and later times. Because the process being summed in both cases is iid, the distributions of both random variables are the same and the sum process can be said to have the stationary increment property. | ||
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=== Answer 2 === | === Answer 2 === | ||
Write it here. | Write it here. | ||
Revision as of 23:32, 14 April 2013
Contents
Practice Problem: Stationary Increment Property
Question
Explain what is the "stationary increment property" and why sum processes have this property.
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
The stationary increment property says that the difference between the values of a random process at two distinct times will result in a random variable with the same distribution as the random variable contained in the random process at the time found by differencing the two distinct times mentioned earlier.
Sum processes have this property because the difference between the values of a sum process at two distinct times yields a random variable defined by summing the values of an iid process from the earlier time until the later time. In addition, the random variable contained in the sum process at the time found by differencing the earlier and later times is found by summing the values of the same iid process from the initial time until the time found by differencing the earlier and later times. Because the process being summed in both cases is iid, the distributions of both random variables are the same and the sum process can be said to have the stationary increment property.
Answer 2
Write it here.
Answer 3
Write it here.
